2024/05/01 by Avital Boruchovsky, Tuvi Etzion, Boruchovsky, Avital +2 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #Cellular Automata and Applications #Coding theory and cryptography #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2405.00258
openalex publication_date 2024/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nearly perfect packing codes are those codes that meet the Johnson upper bound on the size of error-correcting codes. This bound is an improvement to the sphere-packing bound. A related bound for covering codes is known as the van Wee bound. Codes that meet this bound will be called nearly perfect covering codes. In this paper, such codes with covering radius one will be considered. It will be proved that these codes can be partitioned into three families depending on the smallest distance between neighboring codewords. Some of the codes contained in these families will be completely characterized. Other properties of these codes will be considered too. Construction for codes for each such family will be presented, the weight distribution and the distance distribution of codes from these families are characterized. Finally, extended nearly perfect covering code will be considered and unexpected equivalence classes of codes of the three types will be defined based on the extended codes.